(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A certain sound wave has a measured intensity of 40 decibels at a distance of 125 m from the point source where the waves originated. At what distance from the source would the intensity be increased to 70 decibels.

2. Relevant equations

Sound Level (B) = 10 decibels log ( I/ Io)

I = Ps / 4 pi (r^2)

3. The attempt at a solution

40/ 10 = log (I/Io)

10^4 = I / Io

10 ^4 (Io) = I

10 ^4 (Io) = Ps / 4 pi (r^2)

Ps = 10 ^4 (Io) 4 pi (r^2)

so we then we find the new radius

70/10 = log (I/Io)

10^ 7 ( Io) = I

10^ 7 ( Io) = Ps / 4 pi (r^2)

solve for r 2

r2 = √ (Ps / 4 pi (10^7) I o)

r2 = √ (10 ^4 (Io) 4 pi (r^2) ) / (4 pi (10^7) I o)

= 3.9 m

Shouldn't the radius increase by much more. Because 70 Decibels is much louder than 40 Decibels.

I'd figure that it would be by 50 meters or something.

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# Is this correct. Intensity and sound level.

Can you offer guidance or do you also need help?

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